Optimal trajectories for the Aeroassisted Flight Experiment. Part 2: Equations of motion in an inertial system

The determination of optimal trajectories for the aeroassisted flight experiment (AFE) is discussed. The AFE refers to the study of the free flight of an autonomous spacecraft, shuttle-launched and shuttle-recovered. Its purpose is to gather atmospheric entry environmental data for use in designing aeroassisted orbital transfer vehicles (AOTV). It is assumed that: (1) the spacecraft is a particle of constant mass; (2) the Earth is rotating with constant angular velocity; (3) the Earth is an oblate planet, and the gravitational potential depends on both the radial distance and the latitude (harmonics of order higher than four are ignored); and (4) the atmosphere is at rest with respect to the Earth. Under these assumptions, the equations of motion for hypervelocity atmospheric flight (which can be used not only for AFE problems, but also for AOT problems and space shuttle problems) are derived in an inertial system. Transformation relations are supplied which allow one to pass from quantities computed in an inertial system to quantities computed in an Earth-fixed system and vice versa.